Evaluating galaxy dynamical masses from kinematics and jeans equilibrium in simulations

We provide prescriptions to evaluate the dynamical mass (M-dyn) of galaxies from kinematic measurements of stars or gas using analytic considerations and the VELA suite of cosmological zoom-in simulations at z = 1-5. We find that Jeans or hydrostatic equilibrium is approximately valid for galaxies of stellar masses above M-* similar to 10(9.5) M-circle dot out to 5 effective radii (R-e). When both measurements of the rotation velocity v(phi) and of the radial velocity dispersion sigma(r) are available, the dynamical mass M-dyn similar or equal to G(-1) V(c)(2)r, can be evaluated from the Jeans equation V-c(2) = v(phi)(2) + alpha sigma(2)(r) assuming cylindrical symmetry and a constant, isotropic sigma(r). For spheroids, alpha is inversely proportional to the Sersic index n and alpha similar or equal to 2.5 within R-e, (stars) for the simulated galaxies. The prediction for a self-gravitating exponential disc, alpha = 3.36(r/R-e), is invalid in the simulations, where the dominant spheroid causes a weaker gradient from alpha similar or equal to 1 at R-e, (gas) to 4 at 5R(e, gas). The correction in alpha for the stars due to the gradient in sigma(r)(r) is roughly balanced by the effect of the aspherical potential, while the effect of anisotropy is negligible. When only the effective projected velocity dispersion sigma(1) is available, the dynamical mass can be evaluated as M-dyn = K G(-1)R(e)sigma(2)(1), where the virial factor K is derived from alpha, given the inclination and v(phi)/sigma(r). We find that the standard value K = 5 is approximately valid only when averaged over inclinations and for compact and thick discs, as it ranges from 4.5 to above 10 between edge-on and face-on projections.

Automated summary

In this study, dynamical mass of galaxies is evaluated from kinematic measurements of stars or gas using analytic considerations and cosmological zoom-in simulations. It is found that Jeans or hydrostatic equilibrium is valid for galaxies with larger stellar masses, and a formula for evaluating dynamical mass is proposed.